Question

a number cube is rolled three times. an outcome is represented by a string of the sort oee (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). the 8 outcomes are listed in the table below. note that each outcome has the same probability. for each of the three events in the table, check the outcome(s) that are contained in the event. then, in the last column, enter the probability of the event. outcomes probability ooe ooo eeo eoe eee oeo oee eoo event a: exactly one odd number event b: more even numbers than odd numbers event c: alternating even number and odd number (with either coming first)

Explanation:

Step1: Identify Event A outcomes

Count odd numbers in each outcome: EEO (1 odd), EOE (1 odd), OEE (1 odd) → 3 outcomes.

Step2: Calculate Event A probability

Probability = $\frac{\text{Number of Event A outcomes}}{\text{Total outcomes}} = \frac{3}{8}$.

Step3: Identify Event B outcomes

More even than odd (≥2 evens): EEO, EOE, EEE, OEE → 4 outcomes.

Step4: Calculate Event B probability

Probability = $\frac{4}{8} = \frac{1}{2}$.

Step5: Identify Event C outcomes

Alternating (OEO, EOE) → 2 outcomes.

Step6: Calculate Event C probability

Probability = $\frac{2}{8} = \frac{1}{4}$.

Answer:

Event A probability: $\frac{3}{8}$
Event B probability: $\frac{1}{2}$
Event C probability: $\frac{1}{4}$